MEMS resonators are used for a filter circuit, which utilizes electricity passage characteristics between input and output electrodes that improves only in the vicinity of a certain frequency, i.e., the resonance frequency (mechanical resonance frequency) of the vibrator, or a temperature sensor, a pressure sensor, a mass sensor, etc., each of which utilizes the resonance frequency of the vibrator that shifts depending on a temperature, stress applied to the vibrator, or a slight amount of attached extraneous matters to the vibrator, and the like, for example.
In the case where the MEMS resonator is used as a filter of an electric circuit for an HF band, a VHF band, or a UHF band, the vibrator should be finely implemented in size to micrometers or less in order to resonate mechanically in the bands above.
Likewise, in the case where the MEMS resonator is applied to a mass sensor or the like, vibrators with a high mechanical resonance frequency are preferred for detecting a slight amount of mass. This is because that the minimal detectability of mass is proportional to the −2.5th power of its mechanical resonance frequency. That is, vibrators of a fine size such as micrometers or less are also preferable in such applications.
A conventional MEMS resonator is now described with reference to FIGS. 12A and 12B.
FIG. 12A is a perspective view of a principal part of a MEMS resonator 200 prepared by use of a SOI (Silicon On Insulator) substrate. The topmost silicon layer of the SOI substrate is etched to form a beam-type vibrator 201, an input electrode 203, and an output electrode 205. A BOX (Buried OXide film) layer 211 is partially etched to bring the vibrator 201 into a vibratable state, and a both ends supporting part 207 of the vibrator 201, the input electrode 203 and the output electrode 205 are fixed to a silicon substrate 209 by a remaining part of the BOX layer 211.
FIG. 12B is a sectional view along the line A-A′ of FIG. 12A. A principal part of the MEMS resonator 200 is configured as that the two electrodes (input electrode 203 and output electrode 205) are respectively opposed to a side surface of the two side surfaces of the vibrator 201 with a gap gi and a gap go interposed therebetween. One electrode is taken as the input electrode 203 while the other electrode is taken as the output electrode 205, and a direct current potential difference (Vp) is made between the input electrode 203 and the vibrator 201 while the direct current potential difference (Vp) is also made between the output electrode 205 and the vibrator 201. The present figure is a specific example thereof, in which the direct current voltage Vp is applied to the vibrator 201 to realize the direct current potential difference. When an AC voltage (Vi) is applied to the input electrode 203, an exciting force acts on the vibrator 201. The exciting force is derived from a varying electrostatic force due to a variation in potential difference between the input electrode 203 and the vibrator 201. When a frequency of the AC voltage (Vi) agrees with the mechanical resonance frequency of the vibrator 201, the vibrator 201 greatly vibrates and a displacement current (io) in association with the vibration is outputted from the output electrode 205.
When the MEMS resonator is structured in suitable size for the above use, the capacitance made up by the vibrator 201 and the output electrode 205 (capacitance Co in FIG. 12B) is generally small, and it is difficult to obtain a large output current. When the capacitance Co is small, ability to store the electrical charge to be ejected to the output electrode 205 is weak, and, hence, a large output current io cannot be derived. Consequently, the need for taking measures against it such as an addition of a amplifying functionality to a signal processing unit of the next stage that is connected to the output electrode 205 arises.
There are several approaches for making the output current from the MEMS resonator large, and the first one is to make a ratio of change of capacitance with respect to a displacement of the vibrator 201 along the vibrating direction (dCo/dx (x is the vibrating direction of the vibrator) large. The change of capacity is inversely proportional to the square of the distance between the output electrode and the vibrator (the gap go of FIG. 12B). Therefore, this can be achieved by making the distance (gap go) between the output electrode 205 and the vibrator 201 small.
Next, the second approach for making the output current from the MEMS resonator large is to apply large exciting force to the vibrator 201 so that large vibration amplitude, that is, a large vibration velocity is provided. The exciting force acting on the vibrator 201 is inversely proportional to the square of a distance between the vibrator 201 and the input electrode 203 (gap gi of FIG. 12B). Therefore, this can be achieved by making the distance (gap gi) between the vibrator 201 and the input electrode 203 short.
However, it is difficult to produce such a narrow gap, which is typically as narrow as 1 μm or less, accurately and stably.
Next, the third approach for making the output current from the MEMS resonator large is to make the direct current voltage (bias voltage Vp of FIG. 12B) that is applied to the vibrator 201 large.
However, when the bias voltage Vp is increased, discharge may occur as a result of a synergistic effect with the narrowed gap, or a phenomenon that the vibrator bends to adhere to the electrode (203 or 205) only by electrostatic force due to the statically applied DC potential (Vp) may occur.
Hence there are practical limits on narrowing the gap and increasing the bias voltage Vp.
Next, the fourth approach for making the output current from the MEMS resonator large is to apply a large input voltage to the MEMS resonator (vi of FIG. 12B). The amplitude of the vibrator 201 is proportional to the input voltage (vi), and the vibration velocity increases with the increase of the input voltage so that the output current (io) also increases. However, there are limits on applying a large input voltage (vi) to the MEMS resonator. This is because, when the input voltage (vi) having amplitude of a predetermined value or more is applied, a magnitude of the output current exhibits hysteresis with respect to a sweeping direction of a frequency of the input voltage. As a result, a resonance point of an oscillation circuit becomes ill-defined and the frequency stability of an oscillation signal significantly deteriorates. Such nonlinear phenomena are attributable to a pull-in effect by the electrode (203 or 205), in which the vibrator is attracted to the electrode when the distance (gap gi or go) between the vibrator 201 and the electrode (203 or 205) becomes excessively short and the constantly-acting electrostatic force, i.e., the electrostatic force derived from the direct current potential difference Vp, acts on the vibrator 201 excessively. These phenomena are discussed as capacitive bifurcation in Non-Patent Literature 1, for example.
In order to make the MEMS resonator operations stable, it is of importance that the resonator should be operated in the operation range where the capacitive bifurcation is not actualized.
On the other hand, in Patent Literature 1, for the purpose of increasing the output current from the MEMS resonator, a plurality of resonators having the same characteristics are prepared within the MEMS resonator and the plurality of resonators are uniformly excited and output currents from the resonators are bundled up.
Patent Literature 1 discloses a configuration where a plurality of resonators identical with each other is arrayed within the MEMS resonator. Identical excitation input voltage is distributed to input electrodes of the plurality of resonators. The output currents from the plurality of resonators are bundled up and outputted. In other words, the MEMS resonator has a configuration where, on its input side, a plurality of input electrodes 203 are connected parallelly to an input terminal for the input voltage vi, and, on its output side, a plurality of output electrodes 205 are also connected parallelly to an output terminal for the output current. In such an array of the plurality of resonators, although an essential difference in size among the individual resonators due to a processing error causes differences in their resonance frequencies, an effect of a certain degree can be expected if a Q value indicating a resonance sharpness is low and displacement of individual frequencies is small as compared with the degree of unsharpness of the resonating waveform at its peak.
As thus described, according to Patent Literature 1, a certain effect can be expected in that a magnitude of the output current outputted from the MEMS resonator is made larger with respect to a magnitude of the input voltage inputted to the MEMS resonator. However, the problem on the improvement of the operational instability of the MEMS resonator to the magnitude of the input voltage inputted to the MEMS resonator remains unsolved.